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SUMMARY:Amanda Montejano (Universidad Nacional Autonoma de Mexico)
DTSTART:20200603T150000Z
DTEND:20200603T152500Z
DTSTAMP:20260423T011218Z
UID:CANT2020/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/33/
 ">Zero-sum squares in bounded discrepancy $\\{-1\,1\\}$-matrices</a>\nby A
 manda Montejano (Universidad Nacional Autonoma de Mexico) as part of Combi
 natorial and additive number theory (CANT 2021)\n\n\nAbstract\nFor $n\\ge 
 5$\, we prove that every $n\\times n$ $\\{-1\,1\\}$-matrix $M=(a_{ij})$ wi
 th discrepancy \n$\\text{disc}(M)=\\sum a_{ij} \\le n$ contains a zero-sum
  square except for the diagonal matrix (up to symmetries). \nHere\, a squa
 re is a $2\\times 2$ sub-matrix of $M$ with entries $a_{i\,j}\, a_{i+s\,s}
 \, a_{i\,j+s}\, a_{i+s\,j+s}$ \nfor some $s\\ge 1$\, and the diagonal matr
 ix is a matrix with all entries above the diagonal equal to $-1$ \nand all
  remaining entries equal to $1$. In particular\, we show that for $n\\ge 5
 $ every \nzero-sum $n\\times n$ $\\{-1\,1\\}$-matrix contains a zero-sum s
 quare. \n\nJoint work with Edgardo Roldán-Pensado and Alma Arévalo.\n
LOCATION:https://researchseminars.org/talk/CANT2020/33/
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